Archangel of Thune’s last ability triggers just once for each life-gaining event, whether it’s 1 life from Auriok Champion or 6 life from Tavern Swindler.

11/17/2017

If a creature you control is dealt lethal damage at the same time that you gain life, it won’t receive a counter from Archangel of Thune’s last ability in time to save it.

11/17/2017

Each creature with lifelink dealing combat damage causes a separate life-gaining event. For example, if two creatures you control with lifelink deal combat damage at the same time, Archangel of Thune’s last ability will trigger twice. However, if a single creature you control with lifelink deals combat damage to multiple creatures, players, and/or planeswalkers at the same time (perhaps because it has trample or was blocked by more than one creature), the ability will trigger only once.

11/17/2017

In a Two-Headed Giant game, life gained by your teammate won’t cause the ability to trigger, even though it causes your team’s life total to increase.